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Year 11 Assessment Qs Help (1 Viewer)
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Eagle Mum
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The answers you uploaded for questions 18, 20c, 24b & 29b contain the full workings and explanations.
For question 7:
Each 50 gram bar is 760kJ.
Since he ate two bars, he has eaten 1520kJ.
1520kJ is 17.47% of 8700kJ (ie. 1520/8700 = 17.47%)
Therefore, the remaining percentage of the recommended daily energy intake for other food is 82.53% (option D)
Alternatively, (8700 - 1520) / 8700 = 7180 / 8700 = 82.53% (D)
For question 7:
Each 50 gram bar is 760kJ.
Since he ate two bars, he has eaten 1520kJ.
1520kJ is 17.47% of 8700kJ (ie. 1520/8700 = 17.47%)
Therefore, the remaining percentage of the recommended daily energy intake for other food is 82.53% (option D)
Alternatively, (8700 - 1520) / 8700 = 7180 / 8700 = 82.53% (D)
For q18 I don't understand why they didnt use $26.334
For q20c and q24b I don't understand them entirely
For q29b I don't understand why they didnt use 17mg in the working out and only the 28mg and 8mg
Q18 off-peak rate is being used so $26.334 is not used
Q29b The goal is get the closest doses to the nearest mg. As it just turns out using the 17mg would not you nearest mg
True, but the question is not well-considered. After all, the actual dose sought is 22.4 mg, and half a 28 mg tablet plus half a 17 mg tablet is 22.5 mg, which is much closer to the goal dosage.
Given the question says "to the nearest mg", cossine is correct with half a 28 mg plus an 8 mg tablet... but if it asked for the combination closest to the required dose, it would be half of each of a 28 mg and a 17 mg tablet.
Question 20
We are looking at a password that is a word plus two digits. We need to consider the possibilities for the two digit part. Ignoring the word, each of the digits can be 0 or 1 or 2 or ... or 9 (ie. 10 possibilities for each digit) and any of the digits can be followed by any of the digits, so there are 10 x 10 = 100 possibilities for the two digit number at the end of the password.
(a) What is the probability that Mishaal guesses the first digit correctly?
There are two possible (and different) answers to this question, depending on how it is interpreted. If it means: Mishaal guesses a number from 0 to 9 (inclusive), what is the chance that this number matches the first digit from the password, then the answer is
 &= \cfrac{\text{Number of correct outcomes}}{\text{Number of possible outcomes}} \\ &= \cfrac{1}{10} \end{align*})
I hope that this is the interpretation intended. However, I suppose it could mean : Mishaal guesses two digits and the first one is correct but the second is incorrect... I think the above interpretation is correct, but we will need this answer later on, so:
 &= \cfrac{\text{Number of correct outcomes}}{\text{Number of possible outcomes}} \\ &= \cfrac{1 \times 9}{100} \\ &= \cfrac{9}{100} \end{align*})
which can also be calculated using a tree diagram approach, where moving along branches means AND and occurs by multiplication, and moving between branches means OR and occurs by addition:
 \\ &= P(\text{guess first correctly AND guess second incorrectly}) \\ &= P(\text{guess first correctly}) \times P(\text{guess second incorrectly}) \qquad \qquad \text{as AND means multiplying probabilities} \\ &= \cfrac{\text{Number of ways to guess first digit correctly}}{\text{Number of choices for first digit}} \times \cfrac{\text{Number of ways to guess second digit incorrectly}}{\text{Number of choices for second digit}} \\ &= \cfrac{1}{10} \times \cfrac{9}{10} \\ &= \cfrac{9}{100} \end{align*})
(b) What is the probability that Mishaal guesses both digits correctly?
There is only one correct combination of the digits and 100 possible combinations, so
 &= \cfrac{\text{Number of correct outcomes}}{\text{Number of possible outcomes}} \\ &= \cfrac{1}{100} \end{align*})
or, calculated like a tree diagram
 \\ &= P(\text{guess first correctly AND guess second correctly}) \\ &= P(\text{guess first correctly}) \times P(\text{guess second correctly}) \\ &= \cfrac{\text{Number of ways to guess first digit correctly}}{\text{Number of choices for first digit}} \times \cfrac{\text{Number of ways to guess second digit correctly}}{\text{Number of choices for second digit}} \\ &= \cfrac{1}{10} \times \cfrac{1}{10} \\ &= \cfrac{1}{100} \end{align*})
(c) What is the probability that Mishaal guesses only one digit correctly?
The difficulty here is that we don't know if Mishaal guesses the first correctly or the second correctly, but we do know that she guess only one correctly. Calculating like a tree diagram:
 \\ &= P(\text{guess two digits and matches only the first one OR guess two digits and matches only one of them}) \\ &= P(\text{guess two digits and matches only the first one}) + P(\text{guess two digits and matches only the second one}) \qquad \qquad \text{as OR means adding probabilities} \\ &= P(\text{guess first correctly AND guess second incorrectly}) + P(\text{guess first incorrectly AND guess second correctly}) \\ &= \cfrac{9}{100} + P(\text{guess first incorrectly}) \times P(\text{guess second correctly}) \qquad \qquad \text{as we showed above that $P(\text{guess first correctly AND guess second incorrectly}) = \cfrac{9}{100}$} \\ &= \cfrac{9}{100} + \cfrac{9}{10} \times \cfrac{1}{10} \\ &= \cfrac{9}{100} + \cfrac{9}{100} \\ &= \cfrac{18}{100} \\ &= \cfrac{9}{50} \end{align*})
There is an alternative approach possible, by subtracting the possibilities that we know did NOT occur from one:
 \\ &= 1 - P(\text{guess two digits and match neither OR guess two digits and match both}) \\ &= 1 - \bigg[P(\text{guess two digits and match neither}) + P(\text{guess two digits and match both})\bigg] \\ &= 1 - \bigg[P(\text{incorrect on first digit AND incorrect on second digit}) + \cfrac{1}{100}\bigg] \qquad \text{as we found $P(\text{guess two digits and match both}) = \cfrac{1}{100}$ in part (b)} \\ &= 1 - \left[P(\text{guess first incorrectly}) \times P(\text{guess second incorrectly}) + \cfrac{1}{100}\right] \\ &= 1 - \left[\cfrac{9}{100} \times \cfrac{9}{100} + \cfrac{1}{100}\right] \\ &= 1 - \left(\cfrac{81}{100} + \cfrac{1}{100}\right) \\ &= 1 - \cfrac{82}{100} \\ &= \cfrac{100 - 82}{100} \\ &= \cfrac{18}{100} \\ &= \cfrac{9}{50} \end{align*})
We are looking at a password that is a word plus two digits. We need to consider the possibilities for the two digit part. Ignoring the word, each of the digits can be 0 or 1 or 2 or ... or 9 (ie. 10 possibilities for each digit) and any of the digits can be followed by any of the digits, so there are 10 x 10 = 100 possibilities for the two digit number at the end of the password.
(a) What is the probability that Mishaal guesses the first digit correctly?
There are two possible (and different) answers to this question, depending on how it is interpreted. If it means: Mishaal guesses a number from 0 to 9 (inclusive), what is the chance that this number matches the first digit from the password, then the answer is
I hope that this is the interpretation intended. However, I suppose it could mean : Mishaal guesses two digits and the first one is correct but the second is incorrect... I think the above interpretation is correct, but we will need this answer later on, so:
which can also be calculated using a tree diagram approach, where moving along branches means AND and occurs by multiplication, and moving between branches means OR and occurs by addition:
There is only one correct combination of the digits and 100 possible combinations, so
(c) What is the probability that Mishaal guesses only one digit correctly?
The difficulty here is that we don't know if Mishaal guesses the first correctly or the second correctly, but we do know that she guess only one correctly. Calculating like a tree diagram:
Question 24
Regular pay = 8 h @ $45 = 8 x 45 = $360
Overtime = 2 h @ 1.5 x $45 = 2 x 1.5 x 45 = $135
Ordinary pay for the day = 360 + 135 = $495
Extreme heat bonus = 5% x 495 = $24.75
Total pay for the day = ordinary pay + bonus = 495 + 24.75 = $519.75
(b) Week with two 9 h days, three 12 h days, and no extreme heat
Regular pay = $360 per day, from above
Overtime on 9 h days = 1 x 1.5 x 45 = $67.50
Overtime on 12 h days = 2 h @ 1.5 x $45 AND 2 h @ 2 x $45 = 2 x 1.5 x 45 + 2 x 2 x 45 = 135 + 180 = $315
Ordinary pay for the week = Regular pay + overtime = 5 x 360 + 2 x 67.50 + 3 x 315 = 1800 + 135 + 945 = $2,880
The solutions provided use an alternative method whereby overtime is treated more than the actual number of hours, but counted at the standard rate (as opposed to the above, where overtime is counted as the actual hours worked, but paid at a higher rate). Under this approach, you count the number of hours of pay he receives knowing that this is higher than the actual number of hours he worked because overtime is now being treated as extra hours at his standard rate instead of a higher rate for those hours. On this basis:
Working a 9 h day means being paid for 8 h ordinary plus 1 h overtime (1 h at 1.5x) = 8 + 1 x 1.5 = 9. 5 h
Working a 12 h day means being paid for 8 h ordinary plus 4 h overtime (2 h at 1.5x, 2 h at 2x) = 8 + 2 x 1.5 + 2 x 2 = 15 h
Hours of pay for the week = 2 x 9 h day + 3 x 12 h day = 2 x 9.5 + 3 x 15 = 19 + 45 = 64 h
Ordinary pay = 64 x 45 = $2,880.
- Mustafa earns $45 per hour for an 8 hour day
- Overtime is time-and-a-half for the first two hours and double time after that
- 5% bonus for days with extreme heat
Regular pay = 8 h @ $45 = 8 x 45 = $360
Overtime = 2 h @ 1.5 x $45 = 2 x 1.5 x 45 = $135
Ordinary pay for the day = 360 + 135 = $495
Extreme heat bonus = 5% x 495 = $24.75
Total pay for the day = ordinary pay + bonus = 495 + 24.75 = $519.75
(b) Week with two 9 h days, three 12 h days, and no extreme heat
Regular pay = $360 per day, from above
Overtime on 9 h days = 1 x 1.5 x 45 = $67.50
Overtime on 12 h days = 2 h @ 1.5 x $45 AND 2 h @ 2 x $45 = 2 x 1.5 x 45 + 2 x 2 x 45 = 135 + 180 = $315
Ordinary pay for the week = Regular pay + overtime = 5 x 360 + 2 x 67.50 + 3 x 315 = 1800 + 135 + 945 = $2,880
The solutions provided use an alternative method whereby overtime is treated more than the actual number of hours, but counted at the standard rate (as opposed to the above, where overtime is counted as the actual hours worked, but paid at a higher rate). Under this approach, you count the number of hours of pay he receives knowing that this is higher than the actual number of hours he worked because overtime is now being treated as extra hours at his standard rate instead of a higher rate for those hours. On this basis:
Working a 9 h day means being paid for 8 h ordinary plus 1 h overtime (1 h at 1.5x) = 8 + 1 x 1.5 = 9. 5 h
Working a 12 h day means being paid for 8 h ordinary plus 4 h overtime (2 h at 1.5x, 2 h at 2x) = 8 + 2 x 1.5 + 2 x 2 = 15 h
Hours of pay for the week = 2 x 9 h day + 3 x 12 h day = 2 x 9.5 + 3 x 15 = 19 + 45 = 64 h
Ordinary pay = 64 x 45 = $2,880.